Introduction to MatLab

Transcription

1 Introduction to MatLab 1 Introduction to MatLab Graduiertenkolleg Kognitive Neurobiologie Friday, 05 November 2004 Thuseday, 09 Novemer 2004 Kurt Bräuer Institut für Theoretische Physik, Universität Tübingen kurt.braeuer@uni-tuebingen.de, web: Skript: - Graduiertenkolleg Kognitive Neurobiologie

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3 Introduction to MatLab 3 Content 1. Starting MatLab Workspace and m-files Help Vectors and matrices Objects Plots Statistics Data import and export Appendix (Plots and Codes)...19

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5 Introduction to MatLab 5 1. Starting MatLab Possibility 1 Possibility 2 Double-click the MatLab shortcut icon on your Windows desktop. >>cd 'work directory' >>edit explorer -> work directory create a new m-file click a 'm-file' with right mouse button open with, select program matlab.exe, activate 'open always with this program' double-click m-file (opens MatLab in the work directory) >>edit

6 6 2. Workspace and m-files ( a ) >> a = 5 stores value 5 in variable, prints result in workspace 5 ( a ) ( prints value of variable a in workspace) >> a = 5; stores value 5 in variable >> a 5 >> >> t = ' hello world '; >> t ' hello world ' >> whos variable list ( opens editor with m-file ) ( calls function in m-file test) >> edit test test >> test example: our first MatLab program workspace editor >> edit test function test ' hello world ' F5 hello world Exercise Open MatLab Create a new m-file with name 'first' Type the program lines x = 1:20 (,sin( * /5)) plot x x pi

7 Introduction to MatLab 7 3. Help Examples for workspace help Examples for MatLab help menu >> help function >> help if >> help for >> help switch >> help whos Click with left mouse buttom: Menu Contents Using MatLab Mathematics - help by Contents Index Search

8 8 4. Vectors and matrices ( 3) >> x = a 0 0 a abcd,,, are numbers b a b a N 1 N 1 b a b a (Integer, Real, π,e,i, >> x= a: d: b a a+ d a+ 2d b-d b x 3 a+ 2d >> x= a: b a a+ 1 a+ 2 >> x= [ a b c d] a b c d >> x= linspace( abn,, ) a a+ b b n elements >> x= linspace( ab, ) a a+ b b 100 elementes >> A= [1 2 3; 4 5 6] ; ( 2,1) A x N 2 >> A= [ x ; y ] xy, R A R R Vektor y Vektor >> A= [ x y ] x y x R, y R A R ( ) Vektor Vektor x N N >> A= [ x' y' ] ( x' y' ) = xy, R A R R y N N Scalar produkt: >> x* y' = xy n n R, R R n >> A* x' = Amnxn R R, R R n ' M N N M ( ) M N M+ N >> A* B = AmnBnk R R, R R R R n ( ( n n) ) ( ) Point produkt: >> x.* y = xy R, R R ( ) M N N K M K N N N >> A.* B = A B R R, R R R R mn mn 2 ( ( n )) ( ( sin mn )) N functions: >> x.^2 = x R R Exercise ( ) ( ) M N M N M N >> sin A = A R R R R a) Which function is evaluated by N M N M N f = prod( 1: N) (>>'help prod' shows the definition and examples for 'prod') N 2

9 Introduction to MatLab 9 b) Study the results of the commands >> N = ones ( 6) prod ( N,2) ( ( 6,: ), ',' ') (' N' ) (' f ') (' 1' ) ( ) >> for n= 1:6, N n,1: n = 1: n; end >> N >> f = >> plot N f b >> xlabel >> ylabel >> title Test >> whos c) Use A= and B = ci) Calculate the determinant of A (Menu help: MatLab - Using MatLab Matrices and linear algebra Inverses ) cii) Solve the linear system Ax= B (Menu help: MatLab - Using MatLab Matrices and linear algebra Solving linear )

10 10 5. Objects >> hnd = text 0,0,'hello world' x and y Position >> hnd=text(0,0,'hello world') hnd = >> get(hnd) Color = [0 0 0] EraseMode = normal Editing = off Extent = [ ] FontAngle = normal FontName = Helvetica FontSize = [10] FontUnits = points FontWeight = normal HorizontalAlignment = left Position = [0 0 0] Rotation = [0] String = hello world Units = data Interpreter = tex VerticalAlignment = middle BeingDeleted = off ButtonDownFcn = Children = [] Clipping = off CreateFcn = DeleteFcn = BusyAction = queue HandleVisibility = on HitTest = on Interruptible = on Parent = [ ] Selected = off SelectionHighlight = on Tag = Type = text UIContextMenu = [] UserData = [] Visible = on Get possibile properties: >> set( hnd,'horizontalalignment' ) [ {left} center right ] Set possibile properties: >> set( hnd,' HorizontalAlignment',' center',' FontSize',25)

11 Introduction to MatLab 11 Exercise a) Rotate the string 'hello world' by 180 degrees (Rotation is a property of the object 'text'. b) Type in the command >> h= plot ([ 1 0 1,0 ] [ 1 0] ) bi) What different line styles are possible bii) Change the line style and the line width biii) change the y-data to [ ]

12 12 6. Plots >>help plot >> x = linspace(0,2* pi); >> >> >> x = plot x >> y = >> (,sin ( x) ),sin( ) (,' :') plot x x b [ ; ].5*[ ; ] (,,' y' ) or fill( x, y,' y' ) ( Hnd is 'handle' for object) ( ) ( shows object properties) (,' ',' ',' ',10) ( changes object properties) fill x y >> Hnd = >> get Hnd >> set Hnd EdgeColor r LineWidth >> subplot n, m, k rows columns PlotNo >> hold >> hold on off ( overdraw ) ( delete old objects when drawing a new one) >> try, delete( 1, ) end ( delete grafik window 1)

13 Introduction to MatLab 13 Curve fitting Data: ( ) ( ) x= x x x y= y y y fit: 1 2 N Y = a+ bx + cx. N get a, b and c with MatLab:\

14 14 a y' = ( 1 x' ( x.^2 )') b = M c = A A= M \ y' Y = M* A Exercise Create a new m-file 'Plot1' Create the time series t=0..10,y=exp(at) with N elements; Reproduce the plots of Plot1 in the appendix If you don't know how to proceed, look into the program file (after the figure) Use the desktop help and the help menu to get an understanding of the statements

15 Introduction to MatLab Statistics Matlab help page: 'Using Matlab Mathematics Data analysis and statistics' Define an own statistic functions Example: Lineare correlation, r-value We consider two measured quantities The r-value is defind by ( x, y ) i { 1.. N } (7-1) i i Dat

16 16 { } { 1.. N } i ( ) ( xi x)( yi y) i i 1.. N i 1.. N { } ( ) 2 2 [ ] Dat r = 1,1. Dat x x y y Dat i (7-2) It is a measure for the linear correlation between the two measured quantities. Three examples for r-values. The closer the data pairs (x I,y i ) lie on a line the closer is the r-value to 1. MatLab formulation ( ) ( ) ( ) N = 10; Generte a data x= 1: N; y= rand(1, N); ( ) x1 = mean x ; Define r-value y1 = mean y; r = sum(( x- x1).*( y- y1))/... ( sqrt( sum(( x-x1).^2))*... sqrt( sum(( y-y1).^2))); Fig. 7-1 Exercise Create a new m-file 'Stat1' Reproduce the plots of Stat1 in the appendix If you don't know how to proceed, look into the program file (after the figure) Use the desktop help and the help menu to get an understanding of the statements

17 Introduction to MatLab Data import and export Matlab help: 'Using matlab Development environment Importing and exporting -

18 18 Write time series in readable format to file 'TimeSeries.txt' ( ) N = 2^8; Generate time series x= 10* linspace(0,2* pi, N); c= (2*mod(2: N + 1,2)-1).*exp(-.5*(1: N)); y= c*sin((1: N)'* x); Y f _ hnd = fopen(' TimeSeriestxt. ',' w'); for n= 1: length( x) fprintf ( f _ hnd,'%10.5 f; %10.5 f; %10.5 f \ n',... ( ) ( Out to file) = fft( y) Fast Fourier transformation end xn ( ), y( n), Y( n)) fclose( f _ hnd) Exercise Write the Data in m-file 'Stat1' into TimeSeries.Txt Create a new m-file 'ReadSeries.m' Write a code to read the data from TimeSeries.Txt and display them in a diagram Further exercises Create new m-files 'Plot2' and 'Plot3' Reproduce the plots in the appendix

19 Introduction to MatLab 19 Plot 1 9. Appendix (Plots and Codes)

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21 Introduction to MatLab 21

22 22 Statistics 1

23 Introduction to MatLab 23

24 24 Plot 2

25 Introduction to MatLab 25 Plot 3

26 Supplementation Exercise (Fit of arbitrary functions) Create a 'random exponential function' by ( ( ( N) )) y= exp 3sort ran 1: Approximate this function by z = α e β x Tipp: Approximate ( ) ( ) you can display ( ) ( ) y x = log y x by z x = α+ βx. Its an easy way to get a and b. The z = α e β x.

27 Introduction to MatLab 27